Method and system for semi-supervised deep anomaly detection for large-scale industrial monitoring systems based on time-series data utilizing digital twin simulation data

ABSTRACT

A computer-implemented method for detecting an anomalous operating status of a technical system. A training phase obtains a first set of time-series values generated by a digital twin simulation of the technical system for a regular operating status and a second set of time-series values measured by sensors in an anomalous operating status, and adjusts parameters of a machine learning model for detecting the regular operating status and for discriminating data samples of the regular operating status from data samples of the anomalous operating status to generate a trained machine learning model. A monitoring phase obtains a set of multivariate time-series values measured by the sensors, calculates an anomaly score value for determining whether the technical system is in an anomalous operating status based on the obtained set of multi-variate time-series values and the trained machine learning model, and outputs a signal including information on the determined anomalous operating status.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the priority benefit of European applicationserial no. 19203001.3, filed on Oct. 14, 2019. The entirety of theabove-mentioned patent application is hereby incorporated by referenceherein and made a part of this specification.

TECHNICAL FIELD OF THE DISCLOSURE

The invention regards a method for semi-supervised deep anomalydetection on time-series data utilizing digital twin simulation data anda corresponding anomaly detection system. The method and system foranomaly detection concern in particular the field of large-scaleindustrial monitoring systems.

BACKGROUND

Detecting a system failure or an undesired operational state in acomplex technical system is a difficult technical problem. A complextechnical system or a complex machine includes a large number ofelements and components. Direct and indirect interdependencies betweenthe individual components usually do not allow an accurate globalassessment of a current system status, even if appropriate sensornetworks are installed which monitor relevant aspects of the system'soperation. The sensor networks generate a large amount of data includingsensor values. Inspecting the generated sensor data and the complicatedinterdependencies between individual components of the system result ina complex and computationally demanding task to decide if a currentoperating status is an anomalous operating status or undesired operatingstatus on the one hand or a regular operating status on the other hand.

Generally, component failures or complete system failures need to beavoided as this involves a decreased availability of the technicalsystem, and may lead to a significant increase in cost for operating thesystem. Often, precursors of component failures or system failures areobservable in measured sensor data of a monitoring system designed tosupervise the technical system by monitoring its key operatingparameters. It is of paramount importance that relevant signals providedby the monitoring system based on the measured operational parametersare inspected and evaluated. A reliable detection of anomalies in thecomplex technical system is a key requirement to validate the properfunction of the system, to detect problems before a component or systemfailure occurs. The reliable detection of anomalies in the complextechnical system enables to schedule maintenance and repair operationsof the technical system.

A fundamental problem in this field is given by the difficulty toproduce an approach that captures all relevant instances of anomaloussignals. This is the case for a high sensitivity, sometimes called truepositive rate, recall, or probability of detection, of the monitoringsystem that monitors the technical system. Simultaneously, themonitoring system is required to produce only a modest number of falsealarms. This corresponds to the monitoring system not identifying toomany cases of a regular operating status as an anomalous operatingstatus, usually termed a false positive rate.

Known rule-based monitoring systems rely on experts in the fieldimplementing a set of checks and balances to ensure a proper operationof the technical system. The rule-based monitoring systems outputmessages in case of a detected anomaly. It does occur that an anomalousoperating status or various anomalous situations are not properlycaptured by the rules and accordingly remain undetected for an extendedperiod.

If the rule-based monitoring system relies on rules that are formulatedtoo conservatively, the rule-based monitoring systems will generate manyfalse alarms indicating an anomalous operating status although themonitored system is working in its regular and intended operatingstatus. These false alarms may even overwhelm a human system operatorwith signals. This may eventually either result in the human systemoperator ignoring any alarm of the monitoring system, be it indeed afalse alarm or a correct information on an anomalous operating status.

Anomaly detection may use different approaches. A common way relies onutilizing existing expert knowledge in the specific technical field. Anexpert in the field defines feasible ranges of sensor values and anydeviation from these ranges (above a certain threshold) is considered ananomaly. This method has the disadvantage that it is difficult to defineand implement rules and error conditions for usually complex technicalsystems. For complex systems with many interrelated components, therules itself tend to become more complex.

Consequently, it is a demanding task to define a set of rules, whichcaptures at least relevant operating states of the technical systemproperly, and does not include inconsistent or conflicting rules.Additionally, a resource demand for defining these rules and errorconditions for large technical systems including many components growsfast.

An alternate approach to anomaly detection benefits from using the vastincrease in simulation capabilities of recent years. Physical simulationmodels have reached a level of maturity and accuracy that they canreplicate a behaviour of the real technical system. This applies inparticular to applications, which utilize some real-world sensor data,for example, weather patterns. Such accurate physical simulation modelsfor technical systems are usually termed digital twin simulations. Forthe purpose of system monitoring and anomaly detection, digital twinsimulations can be efficiently used by running a digital twin simulationin parallel to the normal operation of the technical system. Both, thedigital twin simulation and the technical system operating in thephysical world, share the same environmental input quantities. It ispossible to compare sensor measurements from the real, physicaltechnical system to a corresponding output from the digital twinsimulator, which allows for the detection of unusual and anomalousstates, which might enable to conclude the occurrence of errors in thereal technical system.

Current applications of digital twin simulation technology to industrialapplications focus on various aspects like elucidating aging phenomenaof the physical machine, support scheduling maintenance operations andenabling predictive maintenance, providing alternatives inwhat-if-scenarios, aiding business decisions and explorations of newbusiness fields, among others. The publication “Leveraging Digital TwinTechnology in Model-Based Systems Engineering” by Madni at al, in:Systems 7(1), 7 (2019) provides examples for this use of digital twinsimulation technology.

Some scenarios employ the digital twin simulation technology running inparallel to the physical technical system with same input values andenvironmental conditions as the physical technical system. The digitaltwin simulation outputs a time-series data that can be compared to thecorresponding time-series data from the physical technical system.Anomalies in the system behaviour of the technical system may then bedetected based on their similarity, for example, as discussed by Filinovet al., in “Multivariate Industrial Time Series with Cyber-AttackSimulation: Fault Detection Using an LSTM-based Predictive Data”, NIPSTime Series Workshop (2016).

The invention therefore targets the problem of devising an anomalydetection system with an acceptable balance between detectionsensitivity and false alarms, which improves the current situation ofsubstantial and continuous fine-tuning of the approaches to achieve therequired balance between detection sensitivity and false alarms.

Data analytics and machine learning techniques have found their way intoapplications in real-world industrial setting. These apply to anomalydetection methods, which can be utilized for learning characteristics ofthe sensor data from the real-world technical system. The learnedcharacteristics convey information, which enables to detect anomaliesand undesired operating states of the technical system. Differentapproaches exist to apply machine learning techniques. Unsupervisedapproaches directly learn the dominant statistics of a measurement dataset acquired for the real-world technical system without any a-prioriinformation. There is, however, no explicit information on what ananomaly or an anomalous operating state is, provided to the model. Themodel makes this distinction based on implicit features of themeasurement data. In contrast, supervised approaches for machinelearning methods operate with a large training data set. The trainingdata set includes data samples of regular operating states and anomalousoperating states that are collected along with labelling informationidentifying the type of each data sample. Therefore, the models can betrained to learn the characteristics of the training data set and thendiscriminate between regular operating states and anomalous operatingstates. The supervised approach requires generating large sets oflabelled training data samples, which is resource consuming andtherefore involves significant time and cost.

In a semi-supervised or weakly supervised approach for a machinelearning method, a large amount of unlabelled data along with a smallset of labelled data is used to train a machine learning model to learnto discriminate between regular operating states and anomalous operatingstates.

SUMMARY

The computer-implemented method for detecting an anomalous operatingstatus of a technical system according to a first aspect comprises stepsof, in a training phase, obtaining a first set of time-series valuesgenerated by a digital twin simulation of the technical system for aregular operating status of the technical system, and obtaining a secondset of time-series values measured by a plurality of sensors, theplurality of sensors configured to monitor a set of operationalparameters of the technical system, wherein the plurality of sensorscollects the second set of time-series values in an anomalous operatingstate of the technical system. The training phase then proceeds byexecuting a training step for adjusting parameters of a machine learningmodel for detecting the regular operating status of the technical systemand for discriminating data samples of the regular operating status fromdata samples of the anomalous operating status by processing triples ofdata samples. Each of the triples of data samples comprises a first datasample, a second data sample and a third data sample. The first andsecond data samples are extracted from the first set of time-seriesvalues, and the third data sample is extracted from the second set oftime-series values to generate a trained machine learning model. In amonitoring phase, the method for detecting an anomalous operating statusof a technical system obtains a set of multivariate time-series valuesmeasured by the plurality of sensors. Then, an anomaly score value iscalculated, the anomaly score value enabling to determine whether thetechnical system is in an anomalous operating status based on theobtained set of measures multi-variate time-series values and thetrained machine learning model. Subsequently, a signal includinginformation on the determined anomalous operating status of thetechnical system is generated and output.

A system according to second aspect of the invention is an anomalydetection system for detecting an anomalous operating status of atechnical system. The anomaly detection system comprises a processor,wherein the processor is configured to run a digital twin simulation ofthe technical system for a regular operating status of the technicalsystem to provide a first set of time-series values generated by thedigital twin simulation The system further includes a plurality ofinterfaces for obtaining a second set of time-series values measured bya plurality of sensors. The plurality of sensors is configured tomonitor a set of operational parameters of the technical system, whereinthe plurality of sensors collects the second set of time-series valuesin an anomalous operating status of the technical system. The systemfurther comprises a memory configured to store a first databasecomprising specific sequences of time-series values of the first set oftime-series values generated by the digital twin simulation, and asecond database comprising specific sequences of time-series values ofthe second set of time-series values measured by the plurality ofsensors. The processor is configured, in a training phase, to execute atraining step by adjusting parameters of a machine learning model fordetecting the regular operating status of the technical system and fordiscriminating data samples of the regular operating status from datasamples of the anomalous operating status by processing triples of datasamples. Each of the triples of data samples comprises a first datasample and a second data sample each generated from the first set oftime-series values, and a third data sample generated from the secondset of time-series values to generate a trained machine learning model.In a monitoring phase, the processor is further configured to obtain aset of multivariate time-series values measured by the plurality ofsensors, subsequently to calculate an anomaly score value fordetermining whether the technical system is in an anomalous operatingstatus based on the obtained set of multi-variate time-series values andthe trained machine learning model. The processor is further configuredto generate a signal including information on the determined anomalousoperating status of the technical system. The anomaly detection systemfurther comprises an output stage for outputting the generated signal.

A non-transitory computer readable medium storing a program causing acomputer or a digital signal processor to execute the steps according toone of the embodiments of the method according to the first aspect ofthe invention.

BRIEF DESCRIPTON OF THE DRAWINGS

The discussion of an embodiment of the invention presented below refersto the annexed drawings.

FIG. 1 provides an overview of the processing sequence of an embodimentof the method.

FIG. 2 illustrates the generation of input vectors forming the basis foranomaly detection according to an embodiment.

FIG. 3 illustrates a first example for feature extraction using sets ofraw time-series values.

FIG. 4 illustrates a second example for feature extraction usingstatistical features calculated on sets of raw time-series values.

FIG. 5 shows the architecture of a deep Siamese neural network used inan embodiment.

FIG. 6 illustrates a first example for an auto-encoder architectureusing a convolutional network auto-encoder.

FIG. 7 illustrates a second example for an auto-encoder architectureusing a fully connected feed-forward auto-encoder.

FIG. 8 provides a schematic representation of a cross-validation processflow.

FIG. 9 illustrates an architecture for determining the raw anomaly scoreof a new data sample.

Same reference signs in different figures denote same or correspondingelements. The discussion of same reference signs in different figures,where considered possible without adversely affecting comprehensibility,is avoided.

DETAILED DESCRIPTION

The invention proposes a novel system for detecting an anomalousoperating status (operating state) and undesired operating states in acomplex technical system (machinery), which is equipped with a sensornetwork, and for which additionally a digital twin simulation for thetechnical system exists. The digital twin simulation for the technicalsystem procures (generates, provides) reliably regular operating statesof the technical system in a virtual sphere. Additionally, a set oflabelled anomaly data samples obtained from the real technical system ina physical sphere is available, which may be significantly smaller innumber. The target for the monitoring system is to achieve very highperformance for detecting an anomalous operating status with a low falsepositive and a high true positive rate, while simultaneously onlyminimal effort for the system operator of the technical system duringsetup and operation of the monitoring system is required. The centralaspect of the invention achieves this target by using large amounts ofdata from the digital twin simulation. The data can be easily producedwith limited human interaction required. The effort to produce thedesired small set of anomalous data samples from the real-world physicaltechnical system is also minimal as the few necessary instances ofanomalous data samples are often available from the operational historyof the technical system.

A good detection performance is achieved by using auto-encoder neuralnetworks, which, even in the unsupervised setting without supervisedtraining data, show good performance for anomaly scores derived from thereconstruction error. This is especially true as a regular large amountof operational data samples from the digital twin simulation enters thetraining phase of the inventive method. Including the few superviseddata samples in the training data set and employing a Siamese autoencoder neural network architecture utilizes all available informationon possible machine states without any further effort for the systemoperator in an efficient manner. The resulting anomaly detection methodfor the real technical system data has an anomaly detection performanceexceeding the performance of state of the art with simultaneouslylimited effort for the system operator in setting up or initializing theanomaly detection method.

It is in particular preferred that the method comprises a step ofcomparing the calculated anomaly score value with a predeterminedthreshold value, and determines an anomalous operating status of thetechnical system in case of the calculated anomaly score value exceedinga threshold value.

Preferably, the triples of data samples constitute a training data set

comprising N triples of data samples. N is an integer numbercorresponding to the number of data samples in the first set oftime-series values. Each triple of data sample includes the first datasample from the first set of time-series values, the second data sample,which is randomly selected from the first set of time-series values, andthe third data sample which is randomly selected from the second set oftime-series values. Thus, the entirety of triples is generated bycombining each data sample from the first set of time-series values witha second data sample, randomly selected from the first set oftime-series values and additionally with a third data sample, randomlyselected from the second set of time-series values.

It is particularly advantageous, when the integer number N of datasamples in the first set of time-series values is larger than an integernumber J of data samples in the second set of time-series values.

An embodiment of the method uses as the machine learning model a Siamesetwin neural network comprising two auto-encoder neural networks AE1 andAE2. The two auto-encoder neural networks AE1, AE2 share a same set andvalues of weights and parameters, which encode sensory input data {rightarrow over (x)} ∈

^(D) into a low-dimensional latent representation vector {right arrowover (l)}=Encode({right arrow over (x)}) ∈

^(L), and also decode the low-dimensional latent representation vector{right arrow over (l)} back into an output signal {right arrow over(y)}=Decode({right arrow over (l)}) ∈

^(D) of the original form of the sensory input data. The weights andparameters of the auto-encoder neural networks AE1, AE2 are trained byminimizing a loss-function, the loss function comprising three parts,

L=a L _(REC) +b L _(PCL) +c L _(CL),   (1)

wherein a>0, b>0, and c>0 are freely adjustable parameters. A first partL_(REC) is a reconstruction error for the digital twin simulation dataas input to a first auto-encoder neural network AE1 of the twoauto-encoder neural networks AE1, AE2:

$\begin{matrix}{L_{REC} = \left. {\frac{1}{N}\sum_{i = 1}^{N}} \middle| {{{Decode}_{1}\left( {{Encode}_{1}\left( {\overset{\rightarrow}{x}}_{i}^{DT} \right)} \right)} - {\overset{\rightarrow}{x}}_{i}^{DT}} \right|^{2}} & (2)\end{matrix}$

A second part L_(PCL) is a partial contrastive loss from anomalous datasamples calculated from a second auto-encoder neural network AE2 of thetwo auto-encoder neural networks AE1, AE2:

$L_{PCL} = {\frac{1}{2}{\max \left( {0,\left. {m - {\frac{1}{N}\sum\limits_{i = 1}^{N}}} \middle| {{{Decode}_{2}\left( {{Encode}_{2}\left( {\overset{\rightarrow}{x}}_{i}^{anomalous} \right)} \right)} - {\overset{\rightarrow}{x}}_{i}^{anomalous}} \right|^{2}} \right)}}$

and a third part L_(CL) is a contrastive loss of latent representationscalculated from the two auto-encoders AE1, AE2,

$\begin{matrix}{{{L_{CL} = \left. {\frac{1}{N}\sum_{i = 1}^{N}} \middle| {{{Encode}_{2}\left( {{\overset{\rightarrow}{x}}_{i}^{DT}}^{\prime} \right)} - {{Encode}_{1}\left( {\overset{\rightarrow}{x}}_{i}^{DT} \right)}} \middle| {}_{2} + \right.}\quad}{\quad{\frac{1}{2} {\max \left( {0,{m - \sqrt{\left. {\frac{1}{N}\sum_{i = 1}^{N}} \middle| {{{Encode}_{2}\left( {\overset{\rightarrow}{x}}_{i}^{anomalous} \right)} - {{Encode}_{1}\left( {\overset{\rightarrow}{x}}_{i}^{DT} \right)}} \right|^{2}}}} \right)}^{2}}}} & (3)\end{matrix}$

A margin m>0 is an adjustable parameter. The training dataset

={p _(i)=({right arrow over (x)} _(i) ^(DT) , {right arrow over (x)}_(i) ^(DT) ′, {right arrow over (x)} _(i) ^(anomalous)), i=1, . . . ,N},   (4)

includes the triples of data samples. Each data sample from the firstset of time-series values includes simulated digital twin data ({rightarrow over (x)}_(i) ^(DT)) that is augmented with the randomly chosendata sample from the same first set of time-series values includingsimulated digital twin data ({right arrow over (x)}_(i) ^(DT)):

{right arrow over (x)} _(i) ^(DT)′=random_select_i({{right arrow over(x)} _(j) ^(DT) , j=1, . . . , N}),   (5)

The randomly chosen third data sample from the first set of time-seriesvalues includes actually measured anomalous data,

{right arrow over (x)} _(i) ^(anomalous)=random_select_i({{right arrowover (x)} _(j) ^(anomalous) , j=1, . . . , A}).   (6)

The freely adjustable parameters a, b, and c in the loss function Laccording to equation (1) can either be chosen to be fixed values duringthe entire (complete) training phase. In particular, the freelyadjustable parameters a, b, and c may be set to a=b=c=1 during theentire training phase. Alternatively, the freely adjustable parametersa, b, and c may be changed over the course of the training phase,thereby increasing an efficiency of the training phase.

For example, the freely adjustable parameters are a=1, b=c=0 during afirst part of the training phase and are a=b=c=1 during a second part ofthe training phase. This provides the effect that the machine learningmodel learns detecting the regular operating status during the firstpart of the training phase. Setting the freely adjustable parameters toa=b=c=1 during the second part of the training phase will subsequentlyrefine the machine learning model to additionally learn to discriminatenormal, regular operating states from anomalous operating states.

The first part of the training phase may be a first half of the trainingphase and the second part of the training phase may be a second half ofthe training phase. Alternatively, the freely adjustable parameters area=1, b=c=0 during the first part of the training phase, the freelyadjustable parameters are a=b=1 and c=0 during the second part of thetraining phase, and the freely adjustable parameters are a=b=c=1 duringa third part of the training phase. The first part of the training phasemay be a first third of the training phase and the second part of thetraining phase may be a second third of the training phase, and thethird part of the training phase may be a final third of the trainingphase.

The method according to an embodiment uses, in the monitoring phase, thecalculated anomaly score value of a new data sample {right arrow over(x)}^(NEW), calculated from the set of multivariate time-series valuesmeasured by the plurality of sensors, which is directly provided by thereconstruction error of the first auto-encoder neural network AE1:

AS _(a)=|Decode₁(Encode₁({right arrow over (x)} ^(NEW)))−{right arrowover (x)} ^(NEW)|²   (7)

Alternatively, the method may, in the monitoring phase, calculate thecalculated anomaly score value of a new data sample {right arrow over(x)}^(NEW) from the set of multivariate time-series values measured bythe plurality of sensors, as a sum of the reconstruction error of thefirst auto-encoder neural network AE1 and an average Euclidean distancebetween a latent representation vector of the new data sample from thefirst auto-encoder neural network AE1 and a set of the latentrepresentation vectors of digital twin simulation data from the trainingphase:

$\begin{matrix}{{{{AS_{b}} = \left| {{{Decode}_{1}\left( {{Encode}_{1}\left( {\overset{\rightarrow}{x}}^{NEW} \right)} \right)} - {\overset{\rightarrow}{x}}^{NEW}} \middle| {}_{2} + \right.}\quad}{\quad{\frac{1}{N^{\prime}}\left( {\sum\limits_{i = 1}^{N^{\prime}}\left| {{{Encode}_{2}\left( {\overset{\rightarrow}{x}}_{i}^{DT} \right)} - {{Encode}_{1}\left( {\overset{\rightarrow}{x}}^{NEW} \right)}} \right|^{2}} \right)^{\frac{1}{2}}}}} & (8)\end{matrix}$

The method according to an embodiment may, in the training phase,generate the data samples from the second set of time-series valuesobtained from a plurality of sensors by first aligning in time eachtime-series values of the second set of time-series values.Subsequently, a step of partitioning in time the time-series values ofthe aligned second set of time-series values from each sensor in a setof overlapping time windows of a predefined window length W isperformed. Then, each data sample from a set of measured time-seriesvalues, starting at a same time of the time-windows over the pluralityof sensors and extending for a predefined window length W over thealigned time-series values over the plurality of sensors is determined.

The method may, when determining each data sample from the set ofmeasured time-series values, process the determined data sample furtherby calculating for each time-window, one or a plurality of statisticalfeatures from measured time-series values of the time-series segmentwithin the time-window, the statistical features including in particularone of a mean value, a standard deviation, a median, various quantiles,a kurtosis, and a skewness.

Alternatively or additionally, the method according to an embodimentcan, when determining each data sample from the set of measuredtime-series values, augment the determined data sample with additionaldata. The additional data can comprise in particular information on aday of the week, a work-hour-indicator, a holiday-indicator or aseasonal indicator, the seasonal indicator in particular specifying aseason.

It is to be noted that the generation and processing of data samples isdetailed above for the case of data samples from the set of measuredtime-series values. The generation of data samples and processing datasamples is preferably done in a similar way for data samples generatedfrom the first set of time-series values.

The anomaly detection system for detecting an anomalous operating statusof a technical system may further include the plurality of sensorsconnected to the interfaces. The plurality of sensors includes sensorsconfigured to determine at least one of a low pressure compressorrotational speed, a high pressure compressor rotational speed, a fuelflow rate, turbine inlet total temperature, a turbine inlet totalpressure, a combustor inlet total temperature, a combustor inlet totalpressure, an exhaust gas total temperature.

The anomaly detection system for detecting an anomalous operating statusof a technical system may be configured to detect anomalous operatingstates of a technical facility management system, or an engine, inparticular a turbofan engine or a dual shaft turbofan engine.

An embodiment of the invention is now discussed using an anomalydetection system for a technical system based on a Siamese auto-encoderneural network.

The application areas of such a systems are complex technical systemswhere multivariate time-series data is recorded during operation of thetechnical system. The multivariate time-series data is acquired by aplurality of sensors arranged in a distributed manner over the technicalsystem. The technical system may be a building, for example, a largefactory complex with its technical infrastructure, or a complex piece ofmachinery such as a twin shaft turbofan engine, which is of a rathercompact layout compared to the abovementioned factory complex. However,both instances of a technical system share key characteristics, whichresult in applying the claimed invention providing essential advantages.

The following discussion of the invention refers to the technical systemas machinery.

The invention uses a digital twin simulation model of the machinerywhich simulates all relevant regular operating states of the machineryand has the same output time-series output signals as the physicalmachinery. A digital twin simulation is a digital replica (virtualentity) of a physical entity. By bridging the physical sphere (realworld) and the virtual sphere (digital world), data is transmittedseamlessly allowing the virtual entity to exist simultaneously with thephysical entity.

The digital twin simulation integrates artificial intelligence, machinelearning and software analytics with spatial network graphs to generatea digital simulation model that updates and changes as its physicalcounterpart changes. The digital twin simulation continuously learns andupdates itself from multiple sources to represent its near real-timestatus, working condition or position. Digital twin simulation usessensor data that conveys various aspects of its operating states, baseson the knowledge from human experts, such as engineers with deep andrelevant industry domain knowledge; from other similar machines; fromother similar fleets of machines; and from the larger systems andenvironment in which the digital twin simulation may be a part of. Adigital twin simulation may also integrate historical data from pastmachinery usage and operating states into its digital model.

In the present context, the digital twin simulation refers to a digitalreplica of the machinery.

FIG. 1 provides an overview of the processing sequence of an embodimentof the method. A more detailed discussion follows with reference toFIGS. 2 to 9.

The method comprises a preparatory phase of generating two databasesfrom measured sensor values from the physical machinery andcorresponding simulated values from the virtual digital twin simulation.Specific aspects of the preparatory phase of generating two databaseswill be discussed with reference to FIGS. 2, 3 and 4.

The method comprises a training phase (preparatory training step). Inthe training phase, the system for detecting an anomalous status of themachinery (anomaly detection system) is trained with a dataset generatedfrom digital twin simulation data samples stored in a first databaseaugmented with data samples collected from the physical machinery storedin a second database. In particular, the training phase of the methodfor detecting an anomalous status of the machinery trains the model withthe data set generated from a large amount of digital twin simulationdata samples of the virtual machinery in the regular operating stateaugmented with the small set of (anomalous) data samples obtained fromthe plurality of sensors monitoring operating parameters of the physicalmachinery in an anomalous operating state.

The first database

comprises N sets of time-series data values {right arrow over (x)}_(j)^(DT) originating from the digital twin simulation of the machinery inthe virtual world,

={{right arrow over (x)} _(j) ^(DT) , j=1, . . . , N}  (9)

and the second database

comprises A sets of time-series data values {right arrow over (x)}_(j)^(anomalous) originating from the physical machinery in the real world,

={{right arrow over (x)} _(j) ^(anomalous) , j=1, . . . , A}  (10)

The method generates in the training phase a training data set

based on the first database and the second database. The training dataset

comprises triples of data samples:

={p _(i)=({right arrow over (x)} _(i) ^(DT) , {right arrow over (x)}_(i) ^(DT) ′, {right arrow over (x)} _(i) ^(anomalous)), i=1, . . . ,N}.   (11)

In each of the triples of data samples constituting the training dataset

, each data sample from the first database (digital twin data set),{right arrow over (x)}_(i) ^(DT), is augmented with a second datasample, {right arrow over (x)}_(i) ^(DT)′ from the same first database,which is randomly selected,

{right arrow over (x)} _(i) ^(DT)′=random_select_i({{right arrow over(x)} _(j) ^(DT) , j=1, . . . , N})   (12)

and one data sample from the data sample {right arrow over (x)}_(i)^(anomalous) from the second data base (physical machinery), which israndomly selected from the data sets stored in the second database,

{right arrow over (x)} _(i) ^(anomalous)=random_select_i({{right arrowover (x)} _(j) ^(anomalous) , j=1, . . . , A}).   (13)

This training data set

is used to train the machine learning model in the training phase forrefining the parameters of the model. The trained machine learning modelgenerated in the training phase forms then the basis for the monitoringphase of the method.

In the monitoring phase, the trained machine learning model is usedduring operation of the machinery on data obtained from the physicalmachinery. This process is illustrated in the lower portion of FIG. 1.

During the monitoring phase, the operating states of the machinery aremonitored by using time-series sensor values acquired by a plurality ofsensors. The values are obtained by the system for detecting ananomalous operating status. The steps S1 to S5 of the monitoring phasemay be performed in in each processing cycle (monitoring cycle) of thecomputer-implemented method for detecting and anomalous operatingstatus.

In step S1, a set of multivariate times-series values from the pluralityof sensors is obtained.

In step S2, the method performs feature extraction on the obtained setof multivariate times-series values. The extracted data sample (new datasample) is then provided to the anomaly detection model for furtherprocessing in step S3. In step S4, an anomaly score value AS indicativeif the machinery is in an anomalous operating status is calculated.

The anomalous score value AS represents a determination value, whichenables to determine if the machinery is indeed in an anomalousoperating status. Determining whether the machinery is in an anomalousoperating status may be performed by comparing the calculated anomalyscore value with a predetermined threshold value. In case the comparisonreveals that the calculated anomaly score value exceeds thepredetermined threshold value, it is determined that the machinery isindeed in an anomalous operating status. If the machinery is determinedto be in the anomalous operating status, the method proceeds to step S5.In step S5, information on the determined anomalous operating status ofthe machinery is generated and the information is subsequently output ina signal.

FIG. 2 illustrates the generation of input vectors forming the basis foranomaly detection according to an embodiment.

The method may execute a pre-processing of the obtained time-series ofvalues, either obtained from the digital twin simulation of themachinery as first time-series of values or measured from the machineryas the second time-series of values, in order to generate data sets tobe used for training of the machine learning model.

FIG. 2 depicts three time-series of values. A first time series ofvalues may represent a first data stream A provided by a first sensorfrom the machinery or a corresponding simulation output stream generatedby the digital twin simulation. A second data stream B and a third datastream C refer to respective data streams obtained from a second andthird sensor of the plurality of sensors.

A time series of values refers to a sequence of measured values, whichare sampled at regular time intervals and converted into a digitalformat.

The first time-series of values obtained from the digital twinsimulation and the second time-series of values obtained from theplurality of sensors are pre-processed in the same manner.

All individual time-series of the multivariate time-series values arealigned with respect to time and a data sample is generated byextracting the time-series values within a time window of a predefinedfixed window length W. The extracted time-series values are then storedin a sample vector {right arrow over (x)}_(i).

A next data sample is extracted by moving the time window by apredetermined time and then selecting the time-series values within theshifted time window. The extracted time-series values are then stored ina sample vector {right arrow over (x)}_(i+1).

FIG. 2 illustrates this approach for a first window position i in timeand a second window position i+1 in time. The time windows for i and i+1are shifted by a predetermined time 1 (stride). Subsequent time windowsfor i+1 and i+2 may be shifted by the predetermined time 1 or by adifferent further predetermined time 2, as indicated in FIG. 2. The timewindows for i and i+1 may partially overlap in time, as depicted with anoverlapping time generating an overlap area 3 in FIG. 2.

FIG. 3 illustrates a first example for feature extraction using sets ofraw time-series values.

The feature extraction according to the first example uses raw-timeseries data. The raw time-series values of the measured curves or thesimulated curves are directly stored in the sample vectors {right arrowover (x)}_(i) as illustrated in FIG. 3.

Alternatively or additionally, the time-series values of each measuredcurve or the time-series values of each simulated curve arepost-processed with an additional statistical feature extraction step.The statistical feature extraction step calculates statistical featuresvalues for each time window based on the time-series values. The datasample vectors {right arrow over (x)}_(i) and {right arrow over(x)}_(i+1) are then generated by using those calculated statisticalfeature values. FIG. 4 illustrates this process of using the additionalstatistical feature extraction step.

Calculating statistical feature values may include calculating at leastone of a mean value, a standard deviation, a median, a Kurtosis, asexamples for statistical functions.

Additionally, it is also possible to include additional contextual,environmental, time-based, and other information in each extracted datasample (data sample vector {right arrow over (x)}_(i)), such as areference to a week-day, a work-day indicator, work-time indicator,seasonal indicator, operating state indicators for components of themachinery. These examples for additional information may be used incombination with either the first example for feature extraction usingsets of raw time-series values or the second example for featureextraction using statistical features calculated on sets of rawtime-series values.

FIG. 4 illustrates the second example for feature extraction usingstatistical features calculated on sets of raw time-series values.

The data samples generated as described above are stored in a datastorage device (memory) in two databases. A first database stores thefirst set of time-series values, which comprises data samples obtainedfrom the digital twin simulation (virtual machinery) in the virtualworld. A second database stores the second set of time-series values,which comprises data samples obtained from the machinery (physicalmachinery) in the real world.

The two separate databases therefore comprise the first database storingdata samples derived from the digital twin simulations, preferably overa large time period and for regular operating states and the seconddatabase for comparatively few data samples from the real-world physicalmachinery in anomalous operating states.

Returning to FIG. 1, the feature extraction process discussed withreference to FIGS. 2, 3 and 4 also applies to the processing in step S2on the new data samples obtained in step S1.

An architecture for the Siamese auto-encoder used in an embodiment ofthe method is shown in FIG. 5.

The Siamese auto-encoder comprises two auto-encoder networks of the same(identical) architecture, a first auto-encoder network AE1 and a secondauto-encoder AE2. The first auto-encoder network AE1 and the secondauto-encoder network AE2 share the same weights and other parameters.

The first auto-encoder network AE1 and the second auto-encoder networkAE2 process the training data set

above during the training phase.

A common approach in the training of deep neural architectures may beapplied for the Siamese auto-encoder. The training data set

is partitioned into several batches and a training of the weights andthe parameters of the first auto-encoder network AE1 and the secondauto-encoder network AE2 can be performed with a stochastic gradientdescent or an Adam optimizer. A loss function L to be minimized duringthe training of the Siamese auto-encoder comprises three terms, whichcontribute to the loss function:

L=a L _(REC) +b L _(PCL) +c L _(CL),   (14)

wherein a, b and c are freely adjustable parameters. In particular, a>0,b>0 and c>0 applies for the (freely) adjustable parameters. A first termL_(REC) is a reconstruction error for the digital twin simulation data.The reconstruction error for the digital twin simulation data targetsthe perfect reconstruction of normal operation data samples as specifiedby the digital twin simulation data. The reconstruction error can becalculated as a mean squared error (MSE) between the input signals andthe output signal of the first auto-encoder network AE1,

$\begin{matrix}{L_{REC} = \left. {\frac{1}{N}\sum\limits_{i = 1}^{N}} \middle| {{{Decode}_{1}\left( {{Encode}_{1}\left( {\overset{\rightarrow}{x}}_{i}^{DT} \right)} \right)} - {\overset{\rightarrow}{x}}_{i}^{DT}} \right|^{2}} & (15)\end{matrix}$

In equation (15), N denotes an integer number corresponding to thenumber of data samples {right arrow over (x)}_(i) ^(DT) of the firstdatabase.

The second term L_(PCL) contributing to the loss function L is a partialcontrastive loss from the anomalous data samples calculated from thesecond auto-encoder AE2,

$\begin{matrix}{{{{L_{PCL} =}\quad}\quad}{\quad{\frac{1}{2} {{\max \left( {0,\left. {m - {\frac{1}{N}\sum\limits_{i = 1}^{N}}} \middle| {{{Decode}_{2}\left( {{Encode}_{2}\left( {\overset{\rightarrow}{x}}_{i}^{anomalous} \right)} \right)} - {\overset{\rightarrow}{x}}_{i}^{anomalous}} \right|^{2}} \right)}.}}}} & (16)\end{matrix}$

The second term L_(PCL) is essentially a negative MSE of the datasamples {right arrow over (x)}_(i) ^(anomalous) in the second database(anomalous data samples). Therefore, the MSE for the anomalous datasamples is maximized as it drives the auto-encoder to have a very largereconstruction error for the anomalous data samples {right arrow over(x)}_(i) ^(anomalous). In equation (16), a margin m>0 is an adjustableparameter and allows only anomalous data samples whose distance is lessthan the radius defined by m to contribute to the loss function L.

The third term L_(CL) contributing to the loss function L is acontrastive loss of the latent representations. The contrastive loss iscalculated from the latent representations of both the firstauto-encoder network AE1 and the second auto-encoder network AE2 as,

$\begin{matrix}{{{{{{{{L_{CL} = \left. {\frac{1}{N}\sum_{i = 1}^{N}} \middle| {{{Encode}_{1}\left( {{\overset{\rightarrow}{x}}_{i}^{DT}}^{\prime} \right)} - {{Encode}_{2}\left( {\overset{\rightarrow}{x}}_{i}^{DT} \right)}} \right|^{2}}\quad} +}\quad}\quad}\quad}\quad}{\quad{\frac{1}{2}{\quad {\quad{{\max\left( {0, m}\quad \right.}{\quad{- \left. \quad\sqrt{\left. {\frac{1}{N}\sum_{i = 1}^{N}} \middle| {{{Encode}_{2}\left( {\overset{\rightarrow}{x}}_{i}^{anomalous} \right)} - {{Encode}_{1}\left( {\overset{\rightarrow}{x}}_{i}^{DT} \right)}} \right|^{2}} \right)^{2}}}}}}}}} & (17)\end{matrix}$

This third term L_(CL) minimizes an Euclidian distances between thelatent representation vectors among data samples {right arrow over(x)}_(i) ^(DT) from the second data base (digital twin data samples)achieved by the first term, while at the same time it maximizes theEuclidian distance of the latent representation vectors between digitaltwin data samples {right arrow over (x)}_(i) ^(DT) and anomalous datasamples {right arrow over (x)}_(i) ^(anomalous) according to the secondterm.

The freely adjustable parameters a, b, and c in the loss function Laccording to equation (14) can be chosen to be fixed values during theentire, complete training phase. In particular, the freely adjustableparameters a, b, and c may be set to a=b=c=1 during the entire trainingphase.

Alternatively the freely adjustable parameters a, b, and c may bechanged over the course of the training phase, thereby increasing anefficiency of the training phase.

For example, the freely adjustable parameters are a=1, b=c=0 during afirst part of the training phase and a=b=c=1 during a second part of thetraining phase. Then the machine learning model learns detecting theregular operating status during the first part of the training phase.Setting the freely adjustable parameters to a=b=c=1 during the secondpart of the training phase results in subsequently refining the machinelearning model, respective its weights and parameters, to additionallylearn discriminating regular operating states from anomalous operatingstates.

The first part of the training phase may be a first half of the trainingphase and the second part of the training phase may be a second half ofthe training phase.

Alternatively, the freely adjustable parameters are a=1, b=c=0 duringthe first part of the training phase, and the freely adjustableparameters are a=b=1 and c=0 during the second part of the trainingphase, and the freely adjustable parameters are a=b=c=1 during a thirdpart of the training phase. The first part of the training phase may bea first third of the training phase and the second part of the trainingphase may be a second third of the training phase. The third part of thetraining phase may be a final third of the training phase.

For the case of raw time-series data values as input, the first andsecond auto-encoder networks AE1, AE2 can be realized as convolutionalneural networks.

In case a statistical feature extraction process is performed on the rawtime-series data values during feature extraction for each time window,the first and second auto-encoder networks AE1, AE2 may be realized asplain fully connected feed-forward neural networks. FIGS. 6 and 7provide example architectures for both cases.

FIG. 6 illustrates a first example for an auto-encoder architectureusing a convolutional network auto-encoder.

FIG. 7 illustrates a second example for an auto-encoder architectureusing a fully connected feed-forward auto-encoder.

Additionally k-fold cross validation techniques with hyper-parameteroptimization may be employed in order to improve performance.

For applying k-fold cross validation techniques with hyper-parameteroptimization, the data set is divided into a training data set, avalidation data set and a test set data set. k-fold cross validationtechniques with hyper-parameter optimization employ a standard searchalgorithm, for example grid search, random search, or more techniqueslike irace for tuning the parameters of the auto-encoder networks AE1,AE2.

López-Ibáñez et al. discloses in “The irace package: Iterated Racing forAutomatic Algorithm Configuration”, Operations Research Perspectives,3:43-58 (2016) details for implementing k-fold cross validationtechniques with hyper-parameter optimization using advanced techniques.

FIG. 8 depicts a schematic representation of an approach applying across-validation process flow. Tuneable parameters of the auto-encodernetworks AE1, AE2 are, for example, a number of channels, kernel sizes,a number of nodes per layer, a number of layers, a type of activationfunctions.

Further parameters, which might be tuned are one or more parameters fromthe pre-processing of the first and second sets of time-series data andfeature extraction and include, for example, a window size W of thetime-windows for the data samples, a window time overlap, apredetermined time between succeeding windows i and i+1, a number andtype of statistical features to be extracted from the time-windows,additional variables to be included into the extracted data samples(feature vectors).

FIG. 9 illustrates a schematic architecture for determining the rawanomaly score value AS of a new data sample during the monitoring phaseof the inventive method.

After completing the training phase, the Siamese auto-encoder basedneural network architecture is efficiently used for generating a rawanomaly score value AS for each novel data sample in an online operationof monitoring the physical machinery.

During the monitoring phase, the raw anomaly score value AS_(a) of a newdata sample {right arrow over (x)}^(NEW) extracted from the sensor dataobtained by the plurality sensors is calculated.

In a first embodiment, the anomaly score value AS is provided directlyas anomaly score value AS_(a) by the reconstruction error L_(REC) of thefirst auto-encoder network AE1 according to equation (15),

AS _(a)=|Decode₁(Encode₁({right arrow over (x)} ^(NEW)))−{right arrowover (x)} ^(NEW)|²   (18)

An alternate second embodiment calculates the anomaly score value AS asanomaly score value AS_(b) by a sum of two terms using equation (19):

$\begin{matrix}{{{{AS_{b}} = \left| {{{Decode}_{1}\left( {{Encode}_{1}\left( {\overset{\rightarrow}{x}}^{NEW} \right)} \right)} - {\overset{\rightarrow}{x}}^{NEW}} \middle| {}_{2} + \right.}\quad}{\quad{\frac{1}{N^{\prime}}{\left( {\sum\limits_{i = 1}^{N^{\prime}}\left| {{{Encode}_{2}\left( {\overset{\rightarrow}{x}}_{i}^{DT} \right)} - {{Encode}_{1}\left( {\overset{\rightarrow}{x}}^{NEW} \right)}} \right|^{2}} \right)^{\frac{1}{2}}.}}}} & (19)\end{matrix}$

The first term (addend) of the sum in equation (19) corresponds to thereconstruction error L_(REC) and the second term (addend) is an averageEuclidean distance between a latent representation vector of the newdata sample {right arrow over (x)}^(NEW) and a set of digital twin datasamples from the training phase. Depending on performance requirementsand accuracy requirements, the set of digital twin data samples from thetraining phase can either be a subset of the digital twin training dataset or the complete training data set

.

The calculated anomaly score value AS, AS_(a), AS_(b) may then be usedfor comparing with the predetermined threshold in order to determine ifthe machinery is in a regular operating status or in an anomalousoperating status.

When introducing the discussion of embodiments of the invention, twopossibilities for technical systems are mentioned: while the cited dualshaft turbofan engine represents a more compact example for complexmachinery, the technical system being an energy management systeminstalled in a building facility represents another example for acomplex technical system. The energy management system is arrangeddistributed over the building facility and includes a system fordetecting an anomalous operating status applying the inventive approach.

The system for detecting an anomalous operating status and the energymanagement system may in particular comprise components as follows:

-   -   a central heating and cooling system. The time-series values can        be flow and return temperatures of the coolant and heating fluid        respectively. Further time-series values describe an energy        consumption of the heating and cooling devices of the central        heating and cooling system;    -   a plurality of air ventilation devices each including an        electric power consumption meter providing further time-series        values;    -   a combined heat and power (CHP or cogeneration) device with        sensors providing time-series values for electrical power        consumption and thermal power output of the cogeneration device        respectively;    -   a weather sensor device providing weather data such as ambient        temperature and air humidity measurement values as time series        values;    -   a photovoltaic system with sensor devices providing time-series        values for electrical power generation;    -   one or more electric vehicle charging stations, each fielding a        sensor for generating time-series values for electrical power        consumption when charging an electric vehicle;    -   further appliances and office devices operating on electric        power and each or at least those with power consumption in a        relevant size with a metering device measuring individual        electric power consumption and providing a respective        time-series data values.

These elements (installations) in the facility are equipped with one ormore sensors, which continuously measure time-series values and generatetime-series data values therefrom. The measured time-series data valuescan be stored in a central monitoring server, which runs a time-seriesdatabase. An implementation for setting up such time series database maybe done using available products such as influxDB, for example.

Such energy management system may show many different types of anomalousoperating states deviating from regular operating states. Types ofanomalous operating states (anomalies) that may occur include:

-   -   a sensor failure: a sensor does not provide an output signal.        This is a major error as it results data loss. However, the        sensor failure is generally easy to detect using standard means.    -   a machine component fails and the associated sensor provides        time-series values with actual value(s) in ranges which are        beyond parameter specifications of the measured parameter. For        example, the heating system ceases to operate. All measured        temperature values will decrease to an ambient temperature        value. All heating pumps stop operating. This can be easy to        detect.    -   a sensor provides measurement values, which represent physically        impossible data. For example, a volume flow sensor of a heating        fluid system shows high fluctuations in time, which is not        physically possible since the fluid circulation inside a pipe        physically cannot change that fast. This error is difficult to        detect as it concerns the statistical properties of a        times-series of measured values.    -   a part of the machinery transitions into one operating status A,        while another part goes into an incompatible operating status B.        For example, the cooling compressors are not operating due to        the absence of a cooling demand, but due to an error, the        circulation and ventilation pumps of the cooling system run at        high levels.    -   unpredictable environmental interference. For example, during an        on-site visit to a machine room, a human operator spontaneously        decides to switch off the cogeneration device installed in this        machine room in order to avoid elevated noise levels in the        machine room. This is in principle not detectable from regular        operating status, except that it then appears that the control        mechanism determining an on- and off-switching of the        cogeneration device appears to have changed status. However,        after the human operator's intervention is reversed, the        cogeneration device and the energy management system returns to        a regular operating status.

For implementing the system for detecting an anomalous operating status,the energy management system and its installations and the facility weremodelled with a digital twin simulation, which is realized is using theModelica-based SimulationX tool together with the Green City library formodelling of building energy systems and e-mobility applications.

Rodemann and Unger provide in “Smart Company Digital Twin—SupportingController Development and Testing Using FMI”, Japanese Society ofAutomotive Engineers Spring Meeting (2018) information for the digitaltwin simulation. The implementation further refers to Unger et al.,“Green Building—Modeling renewable building energy system with eMobilityusing Modelica”, in: Proceedings of Modelica conference (2012) forimplementation details of the Modelica-based SimulationX tool incombination with the Green City library.

The digital twin simulation for the energy management system wereperformed generating time-series values for a time span ranging fromNovember 2017 to May 2019. Real time series-values for weathermeasurement data was used as an input for the simulation. A digital twindata set is generated using the described method steps and stored in thefirst data base. A set of 100 anomalous scenarios for the energymanagement system showing anomalous operating states were collected fromphysical measurements of the physical energy management system duringthe cited period of time, which is covered by the digital twinsimulation. The time-series values for the physical energy managementsystem are stored in the first data base.

The generated first and second time-series values are then used togenerate the training data set

for use in the training phase. Without any further human expertinvolvement, the system for detecting anomalous operating status istrained in the previously described manner. The results of the trainedanomaly detection machine learning system proved a high anomalydetection performance in a test run of the monitoring phase.

What is claimed is:
 1. A computer-implemented method for detecting ananomalous operating status of a technical system, the method comprisingsteps of: in a training phase, obtaining a first set of time-seriesvalues generated by a digital twin simulation of the technical systemfor a regular operating status of the technical system, obtaining asecond set of time-series values measured by a plurality of sensors, theplurality of sensors configured to monitor a set of operationalparameters of the technical system, wherein the plurality of sensorscollects the second set of time-series values in an anomalous operatingstatus of the technical system, executing a training step by adjustingparameters of a machine learning model for detecting the regularoperating status of the technical system and for discriminating datasamples of the regular operating status from data samples of theanomalous operating status by processing triples of data samples, eachof the triples of data samples comprising a first data sample and asecond data sample both taken from the first set of time-series values,and a third data sample taken from the second set of time-series values,to generate a trained machine learning model, and in a monitoring phase,obtaining a set of multivariate time-series values measured by theplurality of sensors, calculating an anomaly score value for determiningwhether the technical system is in an anomalous operating status basedon the obtained set of multi-variate time-series values and the trainedmachine learning model, generating and outputting a signal includinginformation on the determined anomalous operating status of thetechnical system.
 2. The method according to claim 1, wherein the methodcomprises a step of comparing the calculated anomaly score value with apredetermined threshold value, and determining an anomalous operatingstatus of the technical system in case of the calculated anomaly scorevalue exceeding the predetermined threshold value.
 3. The methodaccording to claim 1, wherein the triples of data samples constitute atraining data set (

) comprising N triples of data samples, wherein N is an integer numbercorresponding to the number of data samples in the first set oftime-series values, and each triple of data sample includes the firstdata sample from the first set of time-series values, the second datasample which is randomly selected from the first set of time-seriesvalues, and the third data sample which is randomly selected from thesecond set of time-series values.
 4. The method according to claim 3,wherein the integer number N of data samples in the first set oftime-series values is larger than an integer number J of data samples inthe second set of time-series values.
 5. The method according to claim3, wherein the machine learning model is a Siamese twin neural networkcomprising two auto-encoder neural networks (AE1, AE2), the twoauto-encoder neural networks (AE1, AE2) sharing a same set and values ofweights and parameters, which encode sensory input data {right arrowover (x)} ∈

^(D) into a low-dimensional latent representation vector {right arrowover (l)}=Encode({right arrow over (x)}) ∈

^(L), and decode the low-dimensional latent representation vector {rightarrow over (l)} back into an output signal {right arrow over(y)}=Decode({right arrow over (l)}) ∈

^(D) of the original form of the sensory input data, and wherein theweights and parameters of the auto-encoder neural networks (AE1, AE2)are trained by minimizing a loss-function, the loss function comprisingthree parts,L=aL _(REC) +bL _(PCL) +cL _(CL) wherein a>0, b>0, and c>0 are freelyadjustable parameters and wherein a first part L_(REC) is areconstruction error for the digital twin simulation data as input to afirst auto-encoder neural network (AE1) of the two auto-encoder neuralnetworks (AE1, AE2),$L_{REC} = \left. {\frac{1}{N}\sum\limits_{i = 1}^{N}} \middle| {{{Decode}_{1}\left( {{Encode}_{1}\left( {\overset{\rightarrow}{x}}_{i}^{DT} \right)} \right)} - {\overset{\rightarrow}{x}}_{i}^{DT}} \right|^{2}$and a second part L_(PCL) is a partial contrastive loss from anomalousdata samples calculated from a second auto-encoder neural network (AE2)of the two auto-encoder neural networks (AE1, AE2),$L_{PCL} = {\frac{1}{2}{\max \left( {0,\left. {m - {\frac{1}{N}\sum\limits_{i = 1}^{N}}} \middle| {{{Decode}_{2}\left( {{Encode}_{2}\left( {\overset{\rightarrow}{x}}_{i}^{anomalous} \right)} \right)} - {\overset{\rightarrow}{x}}_{i}^{anomalous}} \right|^{2}} \right)}}$and a third part L_(CL) is a contrastive loss of latent representationscalculated from the two auto-encoders (AE1, AE2),${{{{{{{L_{CL} = \left. {\frac{1}{N}\sum_{i = 1}^{N}} \middle| {{{Encode}_{1}\left( {{\overset{\rightarrow}{x}}_{i}^{DT}}^{\prime} \right)} - {{Encode}_{2}\left( {\overset{\rightarrow}{x}}_{i}^{DT} \right)}} \right|^{2}}\quad} +}\quad}\quad}\quad}\quad}{\quad{\frac{1}{2}{\quad {\quad{{\max\left( {0, m}\quad \right.}{\quad{- \left. \quad\sqrt{\left. {\frac{1}{N}\sum_{i = 1}^{N}} \middle| {{{Encode}_{2}\left( {\overset{\rightarrow}{x}}_{i}^{anomalous} \right)} - {{Encode}_{1}\left( {\overset{\rightarrow}{x}}_{i}^{DT} \right)}} \right|^{2}} \right)^{2}}}}}}}}$where a margin m>0 is an adjustable parameter, the training dataset

={p _(i)=({right arrow over (x)} _(i) ^(DT) , {right arrow over (x)}_(i) ^(DT) ′, {right arrow over (x)} _(i) ^(anomalous)), i=1, . . . ,N}, including the triples of data samples, wherein each data sample fromthe first set of time-series values including simulated digital twindata ({right arrow over (x)}_(i) ^(DT)) is augmented with the randomlychosen data sample from the same first set of time-series valuesincluding simulated digital twin data ({right arrow over (x)}_(i) ^(DT)){right arrow over (x)} _(i) ^(DT)′=random_select_i({{right arrow over(x)} _(j) ^(DT) , j=1, . . . , N}), and the randomly chosen third datasample from the first set of time-series values including actuallymeasured anomalous data,{right arrow over (x)} _(i) ^(anomalous)=random_select_i({{right arrowover (x)} _(j) ^(anomalous) , j=1, . . . , A}).
 6. The method accordingto claim 5, wherein, during the training phase, the freely adjustableparameters a, b, c of the loss function are changed according to apredefined schedule, in particular the freely adjustable parameters area=1, b=c=0 during a first part of the training phase and a=b=c=1 duringa second part of the training phase, or the freely adjustable parametersare a=1, b=c=0 during a first part of the training phase, and a=b=1 andc=0 during a second part of the training phase, and a=b=c=1 during athird part of the training phase.
 7. The method according to claim 5,wherein, in the monitoring phase, the calculated anomaly score value ofa new data sample {right arrow over (x)}^(NEW), calculated from the setof multivariate time-series values measured by the plurality of sensors,is directly given by the reconstruction error of the first auto-encoderneural network (AE1),AS _(a)=|Decode₁(Encode₁({right arrow over (x)} ^(NEW)))−{right arrowover (x)} ^(NEW)|².
 8. The method according to claim 6, wherein, in themonitoring phase, the calculated anomaly score value of a new datasample {right arrow over (x)}^(NEW) calculated from the set ofmultivariate time-series values measured by the plurality of sensors, iscalculated as a sum of the reconstruction error of the firstauto-encoder neural network (AE1) and an average Euclidean distancebetween a latent representation vector of the new data sample from thefirst auto-encoder neural network (AE1) and a set of the latentrepresentation vectors of digital twin simulation data from the trainingphase,${{{AS_{b}} = \left| {{{Decode}_{1}\left( {{Encode}_{1}\left( {\overset{\rightarrow}{x}}^{NEW} \right)} \right)} - {\overset{\rightarrow}{x}}^{NEW}} \middle| {}_{2} + \right.}\quad}{\quad{\frac{1}{N^{\prime}}{\left( {\sum\limits_{i = 1}^{N^{\prime}}\left| {{{Encode}_{2}\left( {\overset{\rightarrow}{x}}_{i}^{DT} \right)} - {{Encode}_{1}\left( {\overset{\rightarrow}{x}}^{NEW} \right)}} \right|^{2}} \right)^{\frac{1}{2}}.}}}$9. The method according to claim 1, wherein, in the training phase, thedata samples are generated from the first and/or the second set oftime-series values obtained from the digital twin simulation or aplurality of sensors, respectively, by aligning in time each time-seriesvalues of the first or second set of time-series values, partitioning intime the time-series values of the aligned time-series values in a setof overlapping time windows of a predefined window length W, determiningeach data sample from a set of aligned time-series values, starting at asame time of the time-windows and extending for a predefined windowlength W over the aligned time-series values.
 10. The method accordingto claim 9, wherein, when determining each data sample from the set oftime-series values, the determined data sample is further processed bycalculating for each time-window, calculating one or a plurality ofstatistical features from time-series values of a time-series segmentwithin the time-window, the statistical features including in particularone of a mean value, a standard deviation, a median, various quantiles,a kurtosis, and a skewness.
 11. The method according to claim 9,wherein, when determining each data sample from the set of time-seriesvalues, augmenting the determined data sample with additional data, theadditional data comprising in particular information on a day of theweek, a work-hour-indicator, a holiday-indicator or a seasonalindicator, the seasonal indicator in particular specifying a season. 12.A non-transitory computer readable medium storing a program causing acomputer or a digital signal processor to execute steps of: in atraining phase, obtaining a first set of time-series values generated bya digital twin simulation of the technical system for a regularoperating status of the technical system, obtaining a second set oftime-series values measured by a plurality of sensors, the plurality ofsensors configured to monitor a set of operational parameters of thetechnical system, wherein the plurality of sensors collects the secondset of time-series values in an anomalous operating status of thetechnical system, executing a training step by adjusting parameters of amachine learning model for detecting the regular operating status of thetechnical system and for discriminating data samples of the regularoperating status from data samples of the anomalous operating status byprocessing triples of data samples, each of the triples of data samplescomprising a first data sample and a second data sample both taken fromthe first set of time-series values, and a third data sample taken fromthe second set of time-series values, to generate a trained machinelearning model, and in a monitoring phase, obtaining a set ofmultivariate time-series values measured by the plurality of sensors,calculating an anomaly score value for determining whether the technicalsystem is in an anomalous operating status based on the obtained set ofmulti-variate time-series values and the trained machine learning model,generating and outputting a signal including information on thedetermined anomalous operating status of the technical system.
 13. Ananomaly detection system for detecting an anomalous operating status ofa technical system, the anomaly detection system comprising: aprocessor, wherein the processor is configured to run a digital twinsimulation of the technical system for a regular operating status of thetechnical system to provide a first set of time-series values generatedby the digital twin simulation, a plurality of sensor interfaces forobtaining a second set of time-series values measured by a plurality ofsensors, the plurality of sensors configured to monitor a set ofoperational parameters of the technical system, wherein the plurality ofsensors collects the second set of time-series values in an anomalousoperating status of the technical system, a memory configured to store afirst data base comprising specific sequences of time-series values ofthe first set of time-series values generated by the digital twinsimulation, and a second data base comprising specific sequences oftime-series values of the second set of time-series values measured bythe plurality of sensors, wherein the processor is configured, in atraining phase, to execute a training step by adjusting parameters of amachine learning model based on the first set of time-series values fordetecting the regular operating status of the technical system, and fordiscriminating data samples of the regular operating status from datasamples of the anomalous operating status by processing triples of datasamples, the each of the triples of data samples comprising a first datasample and a second data sample each from the first set of time-seriesvalues, and a third data sample from the second set of time-seriesvalues to generate a trained machine learning model, and the processoris further configured in a monitoring phase, to obtain a set ofmultivariate time-series values measured by the plurality of sensors, tocalculate an anomaly score value for determining whether the technicalsystem is in an anomalous operating status based on the obtained set ofmulti-variate time-series values and the trained machine learning model,and to generate a signal including information on the determinedanomalous operating status of the technical system, and the anomalydetection system further comprises an output stage for outputting thegenerated signal.
 14. The anomaly detection system for detecting ananomalous operating status of a technical system according to claim 13,wherein the anomaly detection system further comprises the plurality ofsensors connected to the sensor interfaces, wherein the plurality ofsensors includes sensors configured to determine at least one of a lowpressure compressor rotational speed, a high pressure compressorrotational speed, a fuel flow rate, turbine inlet total temperature, aturbine inlet total pressure, a combustor inlet total temperature, acombustor inlet total pressure, an exhaust gas total temperature. 15.The anomaly detection system for detecting an anomalous operating statusof a technical system according to claim 13, wherein the anomalydetection system is configured to detect anomalous operating states of atechnical facility management system, or an engine, in particular aturbofan engine or a dual shaft turbofan engine.